TLDR: based on his Florida experience, we can expect he'd "game the system" on anything possible: running agencies, distributing funding, supreme court nominations (although that's unnecessary right now at the Federal level--nonetheless he seems to think the current conservative majority isn't solid enough), vetoes to get his version of the legislation through, gerrymandering and related election measures to increase his party's seat share, etc. And a good dose of the culture wars to keep the [partisan] public engaged and supportive.
I'm not sure what else DeSantis is considering, but among the things he said (in the piece linked from the Q):
“Republican presidents have accepted the canard that the DOJ and FBI are quote, independent,” DeSantis said. “They are not independent agencies. They are part of the executive branch. They answer to the elected President of the United States.”
That's surely inspired by some form the unitary executive theory.
Proponents of a strongly unitary theory argue that the president possesses all of the executive power and can therefore control subordinate officers and agencies of the executive branch. This implies that the power of Congress to remove executive agencies or officers from Presidential control is limited. Thus, under the strongly unitary executive theory, independent agencies and counsels are unconstitutional to the extent that they exercise discretionary executive power not controlled by the President.
Managed to find a bit more from a Florina newspaper, quoting snippets of DeSantis' book:
Indeed, in his book, “The Courage to Be Free,” DeSantis describes how he used his executive authority against school boards, cruise lines, Disney, universities, race studies, local governments and “activist corporations.” He writes with contempt for free-market Republicans who “caved to the demands of large corporations,” and argues instead for government intervention in issues of speech and personal choice “in a way that protects individuals from these powerful institutions.”
[...] He writes that an “energetic executive” should serve as a check on the power of private businesses, including Big Tech and “traditional corporations,” and he scolds his Republican predecessors, arguing that the way Republicans did business is no longer a sufficient check on the growing influence of the liberal movement. “For years, the default conservative posture has been to limit government and then get out of the way,’’ he writes. “...In this context, elected officials who do nothing more than get out of the way are essentially green-lighting these institutions to continue their unimpeded march through society.” [...] Like Trump, DeSantis has imposed bans on speech relating to gender and diversity at universities. In addition, he has advanced policies that withhold state investments in banks that practice environmental, social and diversity policies. [...]
He threatened Disney, suggesting he would dissolve its special taxing district because of its advocacy on behalf of LBGTQ rights and against his proposals. He banned companies from requiring vaccinations, and battled cruise lines over vaccine passports. And he ousted Hillsborough State Attorney Andrew Warren from office, calling it a “clear signal to other prosecutors around Florida” not to follow Warren’s lead on progressive policies. [...]
He has expanded the scope of his executive authority, issuing hundreds of executive orders each year, and adopted rules to restrict speech and public gatherings. For example, the Florida Department of Management Services last year issued a rule to empower law enforcement to remove from the Capitol demonstrators they think may prove disruptive. This year, the agency issued a new rule banning any organization, including companies and advocacy organizations, from reserving space in the Capitol unless the DeSantis administration has determined that it “aligns” with its mission.
And, of course, to his critics that has another name: "right-wing populist authoritarian":
Mac Stipanovich, a former GOP consultant including for former Florida Gov. Jeb Bush, describes the dominant viewpoint in the Republican Party today as one of “right-wing populist authoritarians.”
DeSantis approach to government is a stark contrast to the Reagan ideal of “the best government is the government closest to the people,’’ he said. “Just look at his savaging of local governments and local voters, whether it’s school boards, city councils or county commissions — he is just dictating everything out of Tallahassee with highly centralized government,’’ he continued. “....DeSantis decides who can come in and can’t come into your business, and what you can and can’t tell your employees when you’re giving them human resources training. “That is about as un-conservative and un-Republican, historically speaking, as you could possibly conceive.”
One of the points that DeSantis' critics miss (IMHO) is that he (like Orbán in Hungary, with whom he's often compared in terms of the "belief in the central importance of cultural war and the need to wage it using state power") had broad support of the legislature in his state. How he'd able to work around that if he doesn't have a majority in [both chambers of] Congress he hasn't been explicit insofar, from what I read.
OTOH, if does get such majority...
“He’s not charming,” says GOP state representative Fiona McFarland. “But he’s a terminator.” [...]
DeSantis’ methods of keeping the legislature in line are not subtle. At one point, a Republican lawmaker was planning to oppose a DeSantis-backed bill until he got a phone call from the governor, who had helped the lawmaker get elected. Without preliminaries, DeSantis barked into the phone, “Do you know why you’re here?”
“Yes,” the startled lawmaker answered. Without saying another word, the governor hung up, two people familiar with the incident told me. Message delivered.
But anyhow, his point about doing government's business (in Florida) is told in his book:
As DeSantis entered office in 2019, the power of Florida’s executive was already at a historic high.
He was determined to use every bit of it. “One of my first orders of business after getting elected was to have my transition team amass an exhaustive list of all the constitutional, statutory, and customary powers of the governor,” he writes in The Courage to Be Free. “I wanted to be sure that I was using every lever available to advance our priorities.” Aides from the time have corroborated this account, describing a thick binder of information that DeSantis proceeded to devour. [...]
DeSantis short-circuited the usual process for state supreme court nominations, allowing him to cement a conservative majority that would be unlikely to overturn his policies, as previous courts had done to his predecessors. He used a new, aggressive interpretation of his powers under state law to remove local elected officials, including Scott Israel, the Broward County sheriff whose response to the Parkland school shooting drew criticism. Previous governors had reserved that right for officials who broke the law, and a state senate special master recommended that Israel be reinstated, but DeSantis pushed through the removal.
And on the rare occasion when Florida legislators weren't with him... "veto".
When it came time to redraw the state’s congressional districts in 2022, legislators proposed a new map that largely preserved the delegation’s balance. A voter-approved constitutional amendment prohibited partisan gerrymandering and sought to protect minority districts, and lawmakers were wary of being slapped down by the courts if they went too far. But DeSantis had read the relevant laws and precedents, and in January 2022 he proposed his own map, which eliminated a majority-Black district in north Florida and gave the GOP a shot at up to four additional seats in Congress.
None too keen on this attempt to usurp their traditional responsibility, legislators ignored DeSantis and passed their own map instead. DeSantis vetoed it. [...]
The redistricting fight was pure DeSantis. “He did that single-handedly—nobody pushed him—and he was relentless,” one current GOP lawmaker told me. Brian Ballard, a powerhouse lobbyist in Tallahassee and D.C. and an ally of both Trump and DeSantis, says the gambit cemented his dominance. “The [state] senate didn’t lay down for him at first. But he showed he was able to use his political popularity in a way that previous governors had not, and it’s brought him incredible power.” [...]
When a locally elected Democratic prosecutor announced he would not enforce DeSantis’ abortion and transgender policies, DeSantis removed him based on his own reading of the relevant statutes. (A court ruled that the rights of the prosecutor had been violated, but that his dismissal could stand.)
And while he could not quite replicate Orban's method of press control, he came up with next best thing possible in the US:
A pair of local digital outlets, Florida’s Voice and the Florida Standard, popped up shortly after DeSantis was elected, helmed by writers with backgrounds in conservative activism. Their funding sources are unknown, but with DeSantis’ help, they frequently break news about the governor, forcing the rest of the press corps to follow their lead.
We can probably expect similar changes to other informal federal equivalents, like the White House press corps etc., if DeSantis is elected.
He also wants to solidify the conservatives lead in the US Supreme Court, hoping to replace Roberts too:
“If you replace a Clarence Thomas with someone like a Roberts or somebody like that then you’re actually gonna see the court move to the left, and you can’t do that. I also think if you look over those eight years, you very well could be called upon to replace Chief Justice John Roberts, and perhaps even, someone like Justice Sotomayor,” DeSantis said.
“So, it is possible that in those eight years we would have the opportunity to fortify justices Alito and Thomas, as well as actually make improvements with those others and if you were able to do that then you would have a 7-2 conservative majority on the Supreme Court that would last a quarter century, so this is big stuff,” he added.